SOLUTION: Solve the problem. Please show your work.
1. The population of a colony of bacteria is growing exponentially according to the function below, where t is the time in hours. How l
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Question 214807: Solve the problem. Please show your work.
1. The population of a colony of bacteria is growing exponentially according to the function below, where t is the time in hours. How long will it take for the population of the colony to grow to 1,000?
B(t)=12*e^(0.2*t)
e=2.718
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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substitute 1000 for B(t) to get:
take the natural log of both sides to get:
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couple of general properties of logarithms are applicable.
the first is:
the second is:
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using the first one, we get:
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using the second one:
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putting this all together, your equation becomes:
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subtract from both sides of this equation to get:
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divide both sides of this equation by to get:
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this becomes:
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solve for t to get:
t = 22.11424315 hours.
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the population should increase to 1000 in 22.11424315 hours.
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substitute in original equation of:
to get:
which becomes:
B(t) = 1000 confirming t = 22.11424315 hours is a good value for t.
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Colony will increase to 1000 in 22.11424315 hours.
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